By Sophie Morel
This ebook stories the intersection cohomology of the Shimura kinds linked to unitary teams of any rank over Q. as a rule, those forms are usually not compact. The intersection cohomology of the Shimura sort linked to a reductive crew G consists of commuting activities of absolutely the Galois team of the reflex box and of the crowd G(Af) of finite adelic issues of G. the second one motion may be studied at the set of complicated issues of the Shimura sort. during this e-book, Sophie Morel identifies the Galois action--at stable places--on the G(Af)-isotypical elements of the cohomology.
Morel makes use of the strategy built by way of Langlands, Ihara, and Kottwitz, that's to check the Grothendieck-Lefschetz fastened element formulation and the Arthur-Selberg hint formulation. the 1st challenge, that of utilizing the fastened element formulation to the intersection cohomology, is geometric in nature and is the thing of the 1st bankruptcy, which builds on Morel's prior paintings. She then turns to the group-theoretical challenge of evaluating those effects with the hint formulation, while G is a unitary workforce over Q. functions are then given. particularly, the Galois illustration on a G(Af)-isotypical part of the cohomology is pointed out at just about all areas, modulo a non-explicit multiplicity. Morel additionally supplies a few effects on base swap from unitary teams to basic linear groups.
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